Working with Samples of Distributions over Convolutional Kernels

Comments

In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
In [2]:
import numpy as np
import tensorflow as tf

import matplotlib.pyplot as plt

from tensorflow.examples.tutorials.mnist import input_data as mnist_data
In [3]:
tf.__version__
Out[3]:
'1.2.1'
In [4]:
sess = tf.InteractiveSession()
In [5]:
mnist = mnist_data.read_data_sets("/home/tiao/Desktop/MNIST")

Extracting /home/tiao/Desktop/MNIST/train-images-idx3-ubyte.gz
Extracting /home/tiao/Desktop/MNIST/train-labels-idx1-ubyte.gz
Extracting /home/tiao/Desktop/MNIST/t10k-images-idx3-ubyte.gz
Extracting /home/tiao/Desktop/MNIST/t10k-labels-idx1-ubyte.gz
In [6]:
# 50 single-channel (grayscale) 28x28 images
x = mnist.train.images[:50].reshape(-1, 28, 28, 1)
x.shape
Out[6]:
(50, 28, 28, 1)
In [7]:
fig, ax = plt.subplots(figsize=(5, 5))

# showing an arbitrarily chosen image
ax.imshow(np.squeeze(x[5], axis=-1), cmap='gray')

plt.show()

Standard 2D Convolution with conv2d

In [8]:
# 32 kernels of size 5x5x1
kernel = tf.truncated_normal([5, 5, 1, 32], stddev=0.1)
kernel.get_shape().as_list()
Out[8]:
[5, 5, 1, 32]
In [9]:
x_conved = tf.nn.conv2d(x, kernel, 
                        strides=[1, 1, 1, 1], 
                        padding='SAME')
x_conved.get_shape().as_list()
Out[9]:
[50, 28, 28, 32]
In [10]:
x_conved[5, ..., 0].eval().shape
Out[10]:
(28, 28)
In [11]:
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

# showing what the 0th filter looks like
ax1.imshow(kernel[..., 0, 0].eval(), cmap='gray')

# show the previous arbitrarily chosen image
# convolved with the 0th filter
ax2.imshow(x_conved[5, ..., 0].eval(), cmap='gray')

plt.show()

Sample from a Distribution over Kernels

In [12]:
# 8x32 kernels of size 5x5x1
kernels = tf.truncated_normal([8, 5, 5, 1, 32], stddev=0.1)
kernels.get_shape().as_list()
Out[12]:
[8, 5, 5, 1, 32]

Approach 1: Map over samples with conv2d

In [13]:
x_tiled = tf.tile(tf.expand_dims(x, 0), [8, 1, 1, 1, 1])
x_tiled.get_shape().as_list()
Out[13]:
[8, 50, 28, 28, 1]
In [19]:
tf.nn.conv2d(x_tiled[0], kernels[0], 
             strides=[1, 1, 1, 1], 
             padding='SAME').get_shape().as_list()
Out[19]:
[50, 28, 28, 32]
In [15]:
x_conved1 = tf.map_fn(lambda args: tf.nn.conv2d(*args, strides=[1, 1, 1, 1], padding='SAME'),
                      elems=(x_tiled, kernels), dtype=tf.float32)
x_conved1.get_shape().as_list()
Out[15]:
[8, 50, 28, 28, 32]

Approach 2: Flattening

In [16]:
kernels_flat = tf.reshape(tf.transpose(kernels, 
                                       perm=(1, 2, 3, 4, 0)), 
                          shape=(5, 5, 1, 32*8))
kernels_flat.get_shape().as_list()
Out[16]:
[5, 5, 1, 256]
In [17]:
x_conved2 = tf.transpose(tf.reshape(tf.nn.conv2d(x, kernels_flat, 
                                                 strides=[1, 1, 1, 1], 
                                                 padding='SAME'), 
                                    shape=(50, 28, 28, 32, 8)), 
                         perm=(4, 0, 1, 2, 3))
x_conved2.get_shape().as_list()
Out[17]:
[8, 50, 28, 28, 32]
In [18]:
tf.reduce_all(tf.equal(x_conved1, x_conved2)).eval()
Out[18]:
True

Variational Inference with Implicit Approximate Inference Models - @fhuszar's Explaining Away Example Pt. 1 (WIP)

Comments

In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
In [70]:
import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Add, Dense, Dot, Input
from keras.optimizers import Adam
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import HTML, SVG, display_html
from tqdm import tnrange, tqdm_notebook
In [3]:
# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')
In [4]:
np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)
In [5]:
K.tf.__version__
Out[5]:
'1.2.1'
In [6]:
LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3
PRETRAIN_EPOCHS = 60

Bayesian Logistic Regression (Synthetic Data)

In [7]:
z_min, z_max = -5, 5
In [8]:
z1, z2 = np.mgrid[z_min:z_max:300j, z_min:z_max:300j]
In [9]:
z_grid = np.dstack((z1, z2))
z_grid.shape
Out[9]:
(300, 300, 2)
In [10]:
prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)
In [11]:
log_prior = prior.logpdf(z_grid)
log_prior.shape
Out[11]:
(300, 300)
In [13]:
np.allclose(log_prior, 
            -.5*np.sum(z_grid**2, axis=2)/PRIOR_VARIANCE \
            -np.log(2*np.pi*PRIOR_VARIANCE))
Out[13]:
True
In [15]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(z1, z2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(z_min, z_max)
ax.set_ylim(z_min, z_max)

plt.show()
In [16]:
x = np.array([0, 5, 8, 12, 50])
In [37]:
def log_likelihood(z, x, beta_0=3., beta_1=1.):
    beta = beta_0 + np.sum(beta_1*np.maximum(0, z**3), axis=-1)
    return -np.log(beta) - x/beta
In [44]:
llhs = log_likelihood(z_grid, x.reshape(-1, 1, 1))
llhs.shape
Out[44]:
(5, 300, 300)
In [59]:
fig, axes = plt.subplots(ncols=len(x), nrows=1, figsize=(20, 4))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(z1, z2, llhs[i,::,::], cmap=plt.cm.magma)

    ax.set_xlim(z_min, z_max)
    ax.set_ylim(z_min, z_max)
    
    ax.set_title('$p(x = {{{0}}} \mid z)$'.format(x[i]))
    ax.set_xlabel('$z_1$')    
    
    if not i:
        ax.set_ylabel('$z_2$')

plt.show()
In [60]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(z1, z2, np.sum(llhs, axis=0), 
                cmap=plt.cm.magma)

ax.set_xlabel('$z_1$')
ax.set_ylabel('$z_2$')

ax.set_xlim(z_min, z_max)
ax.set_ylim(z_min, z_max)

plt.show()
In [61]:
fig, axes = plt.subplots(ncols=len(x), nrows=1, figsize=(20, 4))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(z1, z2,  np.exp(log_prior+llhs[i,::,::]), 
                cmap='magma')

    ax.set_xlim(z_min, z_max)
    ax.set_ylim(z_min, z_max)
    
    ax.set_title('$Zp(z \mid x = {{{0}}})$'.format(x[i]))
    ax.set_xlabel('$z_1$')    
    
    if not i:
        ax.set_ylabel('$z_2$')

plt.show()
In [63]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(z1, z2, 
            np.exp(log_prior+np.sum(llhs, axis=0)), 
            cmap='magma')

ax.set_xlabel('$z_1$')
ax.set_ylabel('$z_2$')

ax.set_xlim(z_min, z_max)
ax.set_ylim(z_min, z_max)

plt.show()

Model Definitions

Density Ratio Estimator (Discriminator) Model

$T_{\psi}(x, z)$

In [84]:
x_input = Input(shape=(1,), name='x')
x_hidden = Dense(10, activation='relu')(x_input)
x_hidden = Dense(20, activation='relu')(x_hidden)
In [85]:
z_input = Input(shape=(LATENT_DIM,), name='z')
z_hidden = Dense(10, activation='relu')(z_input)
z_hidden = Dense(20, activation='relu')(z_hidden)
In [86]:
discrim_hidden = Add()([x_hidden, z_hidden])
discrim_hidden = Dense(10, activation='relu')(discrim_hidden)
discrim_hidden = Dense(20, activation='relu')(discrim_hidden)
discrim_logit = Dense(1, activation=None, 
                       name='logit')(discrim_hidden)
discrim_out = Activation('sigmoid')(discrim_logit)
In [87]:
discriminator = Model(inputs=[x_input, z_input], outputs=discrim_out)
discriminator.compile(optimizer=Adam(lr=LEARNING_RATE),
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])
In [88]:
ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discrim_logit)
In [89]:
SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))
Out[89]:
G 140115456278480 x: InputLayerinput:output:(None, 1)(None, 1)140115456277696 dense_17: Denseinput:output:(None, 1)(None, 10)140115456278480->140115456277696 140115452033176 z: InputLayerinput:output:(None, 2)(None, 2)140115453473064 dense_19: Denseinput:output:(None, 2)(None, 10)140115452033176->140115453473064 140115453258048 dense_18: Denseinput:output:(None, 10)(None, 20)140115456277696->140115453258048 140115452043616 dense_20: Denseinput:output:(None, 10)(None, 20)140115453473064->140115452043616 140115531775392 add_8: Addinput:output:[(None, 20), (None, 20)](None, 20)140115453258048->140115531775392 140115452043616->140115531775392 140115531775168 dense_21: Denseinput:output:(None, 20)(None, 10)140115531775392->140115531775168 140115531775504 dense_22: Denseinput:output:(None, 10)(None, 20)140115531775168->140115531775504 140115543993984 logit: Denseinput:output:(None, 20)(None, 1)140115531775504->140115543993984 140115453098640 activation_2: Activationinput:output:(None, 1)(None, 1)140115543993984->140115453098640
In [105]:
np.ones((32, 5)) + np.ones((16, 5))

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-105-a367db8def8f> in <module>()
----> 1 np.ones((32, 5)) + np.ones((16, 5))

ValueError: operands could not be broadcast together with shapes (32,5) (16,5)
In [112]:
z_grid_ratio = ratio_estimator.predict([np.ones((16, 1)), np.ones((32, 2))])
z_grid_ratio.shape
Out[112]:
(16, 1)

Initial density ratio, prior to any training

In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [ ]:
discriminator.evaluate(prior.rvs(size=5), np.zeros(5))

Approximate Inference Model

$z_{\phi}(x, \epsilon)$

Here we only consider

$z_{\phi}(\epsilon)$

$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$

In [ ]:
inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()

The variational parameters $\phi$ are the trainable weights of the approximate inference model

In [ ]:
phi = inference.trainable_weights
phi
In [ ]:
SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))
In [ ]:
w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape
In [ ]:
eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape
In [ ]:
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))
In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [ ]:
metrics = discriminator.evaluate(inputs, targets)
In [ ]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)
In [ ]:
metrics
In [ ]:
metrics_dict = dict(zip(discriminator.metrics_names, metrics))
In [ ]:
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

metrics_plots = {k:ax1.plot([], label=k)[0] 
                 for k in ['loss']} # discriminator.metrics_names}

ax1.set_xlabel('epoch')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
Discriminator pre-training
In [ ]:
def train_animate(epoch_num, prog_bar, batch_size=200, steps_per_epoch=15):

    # Single training epoch
    
    for step in tnrange(steps_per_epoch, unit='step', leave=False):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    # Plot Metrics
        
    metrics_dict = dict(zip(discriminator.metrics_names, metrics))

    for metric in metrics_plots:
        metrics_plots[metric].set_xdata(np.append(metrics_plots[metric].get_xdata(), 
                                                  epoch_num))    
        metrics_plots[metric].set_ydata(np.append(metrics_plots[metric].get_ydata(), 
                                                  metrics_dict[metric]))
        metrics_plots[metric].set_label('{} ({:.2f})' \
                                        .format(metric, 
                                                metrics_dict[metric]))
    
    ax1.set_xlabel('epoch {:2d}'.format(epoch_num))
    ax1.legend(loc='upper left')

    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(**metrics_dict)

    return list(metrics_plots.values())
In [ ]:
# main training loop is managed by higher-order
# FuncAnimation which makes calls to an `animate` 
# function that encapsulates the logic of single
# training epoch. Has benefit of producing 
# animation but can incur significant overhead
with tqdm_notebook(total=PRETRAIN_EPOCHS, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=PRETRAIN_EPOCHS,
                         interval=200, # 5 fps
                         blit=True)

    anim_html5_video = anim.to_html5_video()
In [ ]:
HTML(anim_html5_video)
In [ ]:
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))
In [ ]:
metrics = discriminator.evaluate(inputs, targets)
In [ ]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)
In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

metrics_dict = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**metrics_dict), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()

Evidence lower bound

In [ ]:
def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)
In [ ]:
y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred
In [ ]:
y_true = K.ones((300, 300, 1))*K.constant(y)
y_true
In [ ]:
llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)
In [ ]:
sess = K.get_session()
In [ ]:
np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))
In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()

Reweight likelihood term!

In [ ]:
def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(2.*log_likelihood-kl_estimate, axis=-1)

    return elbo
In [ ]:
elbo = make_elbo(ratio_estimator)
In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [ ]:
inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)
In [ ]:
inference.compile(loss=inference_loss, 
                  optimizer=Adam(lr=LEARNING_RATE))
In [ ]:
eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
In [ ]:
y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true
In [ ]:
sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))
In [ ]:
inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))

Adversarial Training

In [ ]:
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

global_epoch = 0

loss_plot_inference, = ax1.plot([], label='inference')
loss_plot_discrim, = ax1.plot([], label='discriminator')

ax1.set_xlabel('epoch')
ax1.set_ylabel('loss')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
In [ ]:
def train_animate(epoch_num, prog_bar, batch_size=200, 
                  steps_per_epoch=15):

    global global_epoch, loss_plot_inference, loss_plot_discrim
    
    # Single training epoch

    ## Ratio estimator training
        
    set_trainable(discriminator, True)

    for _ in tnrange(3*50, unit='step', desc='discriminator', 
                     leave=False):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)

    metrics_dict_discrim = dict(zip(discriminator.metrics_names, 
                                    np.atleast_1d(metrics_discrim)))
    
    ## Inference model training
    
    set_trainable(ratio_estimator, False)

    y_tiled = np.tile(y, reps=(BATCH_SIZE, 1))

    for _ in tnrange(1, unit='step', desc='inference', leave=False):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, y_tiled)
        
    metrics_dict_inference = dict(zip(inference.metrics_names, 
                                      np.atleast_1d(metrics_inference)))

    global_epoch += 1
    
    # Plot Loss
 
    loss_plot_inference.set_xdata(np.append(loss_plot_inference.get_xdata(),
                                            global_epoch))
    loss_plot_inference.set_ydata(np.append(loss_plot_inference.get_ydata(), 
                                            metrics_dict_inference['loss']))

    loss_plot_inference.set_label('inference ({:.2f})' \
                                  .format(metrics_dict_inference['loss']))

    loss_plot_discrim.set_xdata(np.append(loss_plot_discrim.get_xdata(),
                                          global_epoch))
    loss_plot_discrim.set_ydata(np.append(loss_plot_discrim.get_ydata(),
                                          metrics_dict_discrim['loss']))

    loss_plot_discrim.set_label('discriminator ({:.2f})' \
                                  .format(metrics_dict_discrim['loss']))
    
    ax1.set_xlabel('epoch {:2d}'.format(global_epoch))
    ax1.legend(loc='upper left')
    
    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss_inference=metrics_dict_inference['loss'],
                         loss_discriminator=metrics_dict_discrim['loss'])

    return loss_plot_inference, loss_plot_discrim
In [ ]:
with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)
In [ ]:
with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)
In [ ]:
with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)
In [ ]:
with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)

Evaluating the model

In [ ]:
w_sample_prior = prior.rvs(size=128)
eps = np.random.randn(256, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(128), np.ones(256)))
In [ ]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)
In [ ]:
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax1.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax1.set_xlabel('$w_1$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

ax2.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap=plt.cm.magma)
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
In [ ]:
eps = np.random.randn(5000, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
In [ ]:
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax1.scatter(*inference.predict(eps[::10]).T, 
            s=4.**2, alpha=.6, cmap='coolwarm_r')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

sns.kdeplot(*inference.predict(eps).T,
            cmap='magma', ax=ax2)

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
In [ ]:

Variational Inference with Implicit Approximate Inference Models (WIP Pt. 9)

Comments

In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
In [2]:
import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.optimizers import Adam
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import HTML, SVG, display_html
from tqdm import tnrange, tqdm_notebook

Using TensorFlow backend.
In [3]:
# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')
In [4]:
np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)
In [5]:
K.tf.__version__
Out[5]:
'1.2.1'
In [6]:
LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3
PRETRAIN_EPOCHS = 60

Bayesian Logistic Regression (Synthetic Data)

In [7]:
w_min, w_max = -5, 5
In [8]:
w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]
In [9]:
w_grid = np.dstack((w1, w2))
w_grid.shape
Out[9]:
(300, 300, 2)
In [10]:
prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)
In [11]:
log_prior = prior.logpdf(w_grid)
log_prior.shape
Out[11]:
(300, 300)
In [12]:
log_prior = -np.sum(w_grid**2, axis=2)/2/PRIOR_VARIANCE
log_prior.shape
Out[12]:
(300, 300)
In [13]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [14]:
x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([  .5, -1.])
In [15]:
X = np.vstack((x1, x2, x3))
X.shape
Out[15]:
(3, 2)
In [16]:
y1 = 1
y2 = 1
y3 = 0
In [17]:
y = np.stack((y1, y2, y3))
y.shape
Out[17]:
(3,)
In [18]:
def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))
In [19]:
llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape
Out[19]:
(300, 300, 3)
In [20]:
fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()
In [21]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [22]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()

Model Definitions

Density Ratio Estimator (Discriminator) Model

$T_{\psi}(x, z)$

Here we consider

$T_{\psi}(w)$

$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$

In [23]:
discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer=Adam(lr=LEARNING_RATE),
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])
In [24]:
ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)
In [25]:
SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))
Out[25]:
G 139900251159464 dense_1_input: InputLayerinput:output:(None, 2)(None, 2)139900250690168 dense_1: Denseinput:output:(None, 2)(None, 10)139900251159464->139900250690168 139900251158064 dense_2: Denseinput:output:(None, 10)(None, 20)139900250690168->139900251158064 139900251160192 logit: Denseinput:output:(None, 20)(None, 1)139900251158064->139900251160192 139900251182920 activation_1: Activationinput:output:(None, 1)(None, 1)139900251160192->139900251182920
In [26]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

Initial density ratio, prior to any training

In [27]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [28]:
discriminator.evaluate(prior.rvs(size=5), np.zeros(5))

5/5 [==============================] - 0s
Out[28]:
[0.53340649604797363, 1.0]

Approximate Inference Model

$z_{\phi}(x, \epsilon)$

Here we only consider

$z_{\phi}(\epsilon)$

$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$

In [29]:
inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

The variational parameters $\phi$ are the trainable weights of the approximate inference model

In [30]:
phi = inference.trainable_weights
phi
Out[30]:
[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]
In [31]:
SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))
Out[31]:
G 139900250463256 dense_3_input: InputLayerinput:output:(None, 3)(None, 3)139900250462024 dense_3: Denseinput:output:(None, 3)(None, 10)139900250463256->139900250462024 139900250461520 dense_4: Denseinput:output:(None, 10)(None, 20)139900250462024->139900250461520 139900251331832 dense_5: Denseinput:output:(None, 20)(None, 2)139900250461520->139900251331832
In [32]:
w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape
Out[32]:
(200, 2)
In [33]:
eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape
Out[33]:
(200, 2)
In [34]:
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))
In [35]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [36]:
metrics = discriminator.evaluate(inputs, targets)

 32/400 [=>............................] - ETA: 0s
In [37]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)
In [38]:
metrics
Out[38]:
[0.65425197124481205, 0.58999999999999997]
In [39]:
metrics_dict = dict(zip(discriminator.metrics_names, metrics))
In [40]:
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

metrics_plots = {k:ax1.plot([], label=k)[0] 
                 for k in ['loss']} # discriminator.metrics_names}

ax1.set_xlabel('epoch')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
Discriminator pre-training
In [41]:
def train_animate(epoch_num, prog_bar, batch_size=200, steps_per_epoch=15):

    # Single training epoch
    
    for step in tnrange(steps_per_epoch, unit='step', leave=False):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    # Plot Metrics
        
    metrics_dict = dict(zip(discriminator.metrics_names, metrics))

    for metric in metrics_plots:
        metrics_plots[metric].set_xdata(np.append(metrics_plots[metric].get_xdata(), 
                                                  epoch_num))    
        metrics_plots[metric].set_ydata(np.append(metrics_plots[metric].get_ydata(), 
                                                  metrics_dict[metric]))
        metrics_plots[metric].set_label('{} ({:.2f})' \
                                        .format(metric, 
                                                metrics_dict[metric]))
    
    ax1.set_xlabel('epoch {:2d}'.format(epoch_num))
    ax1.legend(loc='upper left')

    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(**metrics_dict)

    return list(metrics_plots.values())
In [42]:
# main training loop is managed by higher-order
# FuncAnimation which makes calls to an `animate` 
# function that encapsulates the logic of single
# training epoch. Has benefit of producing 
# animation but can incur significant overhead
with tqdm_notebook(total=PRETRAIN_EPOCHS, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=PRETRAIN_EPOCHS,
                         interval=200, # 5 fps
                         blit=True)

    anim_html5_video = anim.to_html5_video()



















In [43]:



    


HTML(anim_html5_video)




















Out[43]:

























In [44]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [45]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [46]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [47]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

metrics_dict = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**metrics_dict), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Evidence lower bound













In [48]:



    


def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)

















In [49]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[49]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [50]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[50]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [51]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [52]:



    


sess = K.get_session()

















In [53]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[53]:








True



















In [54]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Reweight likelihood term!













In [55]:



    


def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(2.*log_likelihood-kl_estimate, axis=-1)

    return elbo

















In [56]:



    


elbo = make_elbo(ratio_estimator)

















In [57]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [58]:



    


inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)

















In [59]:



    


inference.compile(loss=inference_loss, 
                  optimizer=Adam(lr=LEARNING_RATE))

















In [60]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [61]:



    


y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[61]:








<tf.Tensor 'concat:0' shape=(200, 3) dtype=float32>



















In [62]:



    


sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))




















Out[62]:








-4.4352226



















In [63]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/200 [===>..........................] - ETA: 0s










Out[63]:








4.4352222633361817

























Adversarial Training













In [64]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

global_epoch = 0

loss_plot_inference, = ax1.plot([], label='inference')
loss_plot_discrim, = ax1.plot([], label='discriminator')

ax1.set_xlabel('epoch')
ax1.set_ylabel('loss')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [121]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, 
                  steps_per_epoch=15):

    global global_epoch, loss_plot_inference, loss_plot_discrim
    
    # Single training epoch

    ## Ratio estimator training
        
    set_trainable(discriminator, True)

    for _ in tnrange(3*50, unit='step', desc='discriminator', 
                     leave=False):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)

    metrics_dict_discrim = dict(zip(discriminator.metrics_names, 
                                    np.atleast_1d(metrics_discrim)))
    
    ## Inference model training

    print('Before:')
    print(ratio_estimator.get_weights()[0])
    print(inference.get_weights()[0])
    
    set_trainable(ratio_estimator, False)

    y_tiled = np.tile(y, reps=(BATCH_SIZE, 1))

    for _ in tnrange(1, unit='step', desc='inference', leave=False):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, y_tiled)

    print('After:')
    print(ratio_estimator.get_weights()[0])
    print(inference.get_weights()[0])
        
    print('###')
        
    metrics_dict_inference = dict(zip(inference.metrics_names, 
                                      np.atleast_1d(metrics_inference)))

    global_epoch += 1
    
    # Plot Loss
 
    loss_plot_inference.set_xdata(np.append(loss_plot_inference.get_xdata(),
                                            global_epoch))
    loss_plot_inference.set_ydata(np.append(loss_plot_inference.get_ydata(), 
                                            metrics_dict_inference['loss']))

    loss_plot_inference.set_label('inference ({:.2f})' \
                                  .format(metrics_dict_inference['loss']))

    loss_plot_discrim.set_xdata(np.append(loss_plot_discrim.get_xdata(),
                                          global_epoch))
    loss_plot_discrim.set_ydata(np.append(loss_plot_discrim.get_ydata(),
                                          metrics_dict_discrim['loss']))

    loss_plot_discrim.set_label('discriminator ({:.2f})' \
                                  .format(metrics_dict_discrim['loss']))
    
    ax1.set_xlabel('epoch {:2d}'.format(global_epoch))
    ax1.legend(loc='upper left')
    
    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss_inference=metrics_dict_inference['loss'],
                         loss_discriminator=metrics_dict_discrim['loss'])

    return loss_plot_inference, loss_plot_discrim

















In [122]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























 
 





















 
 





















Before:
[[ 0.4   0.69 -0.56 -0.45  0.03  0.23 -0.67 -0.19  0.21  0.71]
 [-0.33 -0.29  0.22  0.54 -0.58 -1.03 -0.29 -0.75  0.8  -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.02  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.21 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]

















 
 





















After:
[[ 0.4   0.69 -0.56 -0.45  0.03  0.23 -0.67 -0.19  0.21  0.71]
 [-0.33 -0.29  0.22  0.54 -0.58 -1.03 -0.29 -0.75  0.8  -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.02  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.21 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]
###

















 
 





















Before:
[[ 0.43  0.7  -0.54 -0.43  0.04  0.23 -0.68 -0.18  0.25  0.71]
 [-0.32 -0.28  0.18  0.53 -0.56 -1.02 -0.29 -0.75  0.8  -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.02  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.21 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]

















 
 





















After:
[[ 0.43  0.7  -0.54 -0.43  0.04  0.23 -0.68 -0.18  0.25  0.71]
 [-0.32 -0.28  0.18  0.53 -0.56 -1.02 -0.29 -0.75  0.8  -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]
###

















 
 





















Before:
[[ 0.43  0.7  -0.52 -0.42  0.05  0.23 -0.68 -0.18  0.24  0.7 ]
 [-0.34 -0.28  0.2   0.55 -0.54 -1.03 -0.29 -0.74  0.79 -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]

















 
 





















After:
[[ 0.43  0.7  -0.52 -0.42  0.05  0.23 -0.68 -0.18  0.24  0.7 ]
 [-0.34 -0.28  0.2   0.55 -0.54 -1.03 -0.29 -0.74  0.79 -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]
###

















 
 





















Before:
[[ 0.42  0.71 -0.54 -0.41  0.07  0.23 -0.67 -0.13  0.25  0.71]
 [-0.32 -0.28  0.18  0.55 -0.58 -1.02 -0.3  -0.79  0.81 -0.23]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]

















 
 





















After:
[[ 0.42  0.71 -0.54 -0.41  0.07  0.23 -0.67 -0.13  0.25  0.71]
 [-0.32 -0.28  0.18  0.55 -0.58 -1.02 -0.3  -0.79  0.81 -0.23]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]
###

















 
 





















Before:
[[ 0.39  0.7  -0.52 -0.4   0.06  0.23 -0.67 -0.15  0.27  0.7 ]
 [-0.36 -0.28  0.2   0.52 -0.56 -1.03 -0.3  -0.74  0.8  -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.21 -0.67 -0.61  0.53]]

















 
 





















After:
[[ 0.39  0.7  -0.52 -0.4   0.06  0.23 -0.67 -0.15  0.27  0.7 ]
 [-0.36 -0.28  0.2   0.52 -0.56 -1.03 -0.3  -0.74  0.8  -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.22 -0.67 -0.61  0.53]]
###

















 
 





















Before:
[[ 0.37  0.67 -0.54 -0.44  0.05  0.24 -0.68 -0.15  0.27  0.7 ]
 [-0.39 -0.32  0.2   0.52 -0.56 -1.04 -0.3  -0.73  0.81 -0.21]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.78  0.12  0.65 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.12 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.22 -0.67 -0.61  0.53]]

















 
 





















After:
[[ 0.37  0.67 -0.54 -0.44  0.05  0.24 -0.68 -0.15  0.27  0.7 ]
 [-0.39 -0.32  0.2   0.52 -0.56 -1.04 -0.3  -0.73  0.81 -0.21]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.77  0.12  0.65 -0.31]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.13 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.22 -0.67 -0.61  0.53]]
###

















 
 





















Before:
[[ 0.39  0.68 -0.51 -0.42  0.05  0.23 -0.68 -0.17  0.27  0.71]
 [-0.37 -0.28  0.19  0.5  -0.54 -1.03 -0.3  -0.74  0.83 -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.77  0.12  0.65 -0.31]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.13 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.22 -0.67 -0.61  0.53]]

















 
 





















After:
[[ 0.39  0.68 -0.51 -0.42  0.05  0.23 -0.68 -0.17  0.27  0.71]
 [-0.37 -0.28  0.19  0.5  -0.54 -1.03 -0.3  -0.74  0.83 -0.22]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.77  0.12  0.65 -0.31]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.13 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.22 -0.67 -0.61  0.53]]
###

















 
 





















Before:
[[ 0.38  0.7  -0.56 -0.44  0.03  0.21 -0.67 -0.15  0.23  0.71]
 [-0.36 -0.27  0.2   0.51 -0.55 -1.01 -0.29 -0.74  0.81 -0.2 ]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.77  0.12  0.65 -0.31]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.13 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.22 -0.67 -0.61  0.53]]

















 
 





















After:
[[ 0.38  0.7  -0.56 -0.44  0.03  0.21 -0.67 -0.15  0.23  0.71]
 [-0.36 -0.27  0.2   0.51 -0.55 -1.01 -0.29 -0.74  0.81 -0.2 ]]
[[-0.33 -0.64  0.37 -0.19 -0.02  0.01  0.77  0.12  0.66 -0.3 ]
 [ 0.41 -0.5   0.5   0.17 -0.22 -0.41  0.61 -0.13 -0.13 -0.68]
 [ 0.71 -0.47 -0.69 -0.42 -0.21  0.41  0.22 -0.67 -0.61  0.53]]
###


















---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-122-ab938e4e4048> in <module>()
      9                          blit=True)
     10 
---> 11     anim_html5_video = anim.to_html5_video()
     12 
     13 HTML(anim_html5_video)

~/.virtualenvs/implicit/lib/python3.5/site-packages/matplotlib/animation.py in to_html5_video(self)
   1207                                 bitrate=rcParams['animation.bitrate'],
   1208                                 fps=1000. / self._interval)
-> 1209                 self.save(f.name, writer=writer)
   1210 
   1211             # Now open and base64 encode

~/.virtualenvs/implicit/lib/python3.5/site-packages/matplotlib/animation.py in save(self, filename, writer, fps, dpi, codec, bitrate, extra_args, metadata, extra_anim, savefig_kwargs)
   1060                     for anim, d in zip(all_anim, data):
   1061                         # TODO: See if turning off blit is really necessary
-> 1062                         anim._draw_next_frame(d, blit=False)
   1063                     writer.grab_frame(**savefig_kwargs)
   1064 

~/.virtualenvs/implicit/lib/python3.5/site-packages/matplotlib/animation.py in _draw_next_frame(self, framedata, blit)
   1097         # post- draw, as well as the drawing of the frame itself.
   1098         self._pre_draw(framedata, blit)
-> 1099         self._draw_frame(framedata)
   1100         self._post_draw(framedata, blit)
   1101 

~/.virtualenvs/implicit/lib/python3.5/site-packages/matplotlib/animation.py in _draw_frame(self, framedata)
   1560         # Call the func with framedata and args. If blitting is desired,
   1561         # func needs to return a sequence of any artists that were modified.
-> 1562         self._drawn_artists = self._func(framedata, *self._args)
   1563         if self._blit:
   1564             if self._drawn_artists is None:

<ipython-input-121-78d9a9e0159c> in train_animate(epoch_num, prog_bar, batch_size, steps_per_epoch)
     78     ax2.cla()
     79 
---> 80     w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
     81     w_grid_ratio = w_grid_ratio.reshape(300, 300)
     82 

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/engine/training.py in predict(self, x, batch_size, verbose)
   1515         f = self.predict_function
   1516         return self._predict_loop(f, ins,
-> 1517                                   batch_size=batch_size, verbose=verbose)
   1518 
   1519     def train_on_batch(self, x, y,

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/engine/training.py in _predict_loop(self, f, ins, batch_size, verbose)
   1139                 ins_batch = _slice_arrays(ins, batch_ids)
   1140 
-> 1141             batch_outs = f(ins_batch)
   1142             if not isinstance(batch_outs, list):
   1143                 batch_outs = [batch_outs]

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/backend/tensorflow_backend.py in __call__(self, inputs)
   2263                 value = (indices, sparse_coo.data, sparse_coo.shape)
   2264             feed_dict[tensor] = value
-> 2265         session = get_session()
   2266         updated = session.run(self.outputs + [self.updates_op],
   2267                               feed_dict=feed_dict,

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/backend/tensorflow_backend.py in get_session()
    166     if not _MANUAL_VAR_INIT:
    167         with session.graph.as_default():
--> 168             _initialize_variables()
    169     return session
    170 

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/backend/tensorflow_backend.py in _initialize_variables()
    334     uninitialized_variables = []
    335     for v in variables:
--> 336         if not hasattr(v, '_keras_initialized') or not v._keras_initialized:
    337             uninitialized_variables.append(v)
    338             v._keras_initialized = True

KeyboardInterrupt: 


















In [67]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 































Out[67]:

























In [68]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





































---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-68-ab938e4e4048> in <module>()
      9                          blit=True)
     10 
---> 11     anim_html5_video = anim.to_html5_video()
     12 
     13 HTML(anim_html5_video)

~/.virtualenvs/implicit/lib/python3.5/site-packages/matplotlib/animation.py in to_html5_video(self)
   1207                                 bitrate=rcParams['animation.bitrate'],
   1208                                 fps=1000. / self._interval)
-> 1209                 self.save(f.name, writer=writer)
   1210 
   1211             # Now open and base64 encode

~/.virtualenvs/implicit/lib/python3.5/site-packages/matplotlib/animation.py in save(self, filename, writer, fps, dpi, codec, bitrate, extra_args, metadata, extra_anim, savefig_kwargs)
   1060                     for anim, d in zip(all_anim, data):
   1061                         # TODO: See if turning off blit is really necessary
-> 1062                         anim._draw_next_frame(d, blit=False)
   1063                     writer.grab_frame(**savefig_kwargs)
   1064 

~/.virtualenvs/implicit/lib/python3.5/site-packages/matplotlib/animation.py in _draw_next_frame(self, framedata, blit)
   1097         # post- draw, as well as the drawing of the frame itself.
   1098         self._pre_draw(framedata, blit)
-> 1099         self._draw_frame(framedata)
   1100         self._post_draw(framedata, blit)
   1101 

~/.virtualenvs/implicit/lib/python3.5/site-packages/matplotlib/animation.py in _draw_frame(self, framedata)
   1560         # Call the func with framedata and args. If blitting is desired,
   1561         # func needs to return a sequence of any artists that were modified.
-> 1562         self._drawn_artists = self._func(framedata, *self._args)
   1563         if self._blit:
   1564             if self._drawn_artists is None:

<ipython-input-65-5bea53f24968> in train_animate(epoch_num, prog_bar, batch_size, steps_per_epoch)
     16 
     17         eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
---> 18         w_sample_posterior = inference.predict(eps)
     19 
     20         inputs = np.vstack((w_sample_prior, w_sample_posterior))

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/models.py in predict(self, x, batch_size, verbose)
    907         if self.model is None:
    908             self.build()
--> 909         return self.model.predict(x, batch_size=batch_size, verbose=verbose)
    910 
    911     def predict_on_batch(self, x):

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/engine/training.py in predict(self, x, batch_size, verbose)
   1515         f = self.predict_function
   1516         return self._predict_loop(f, ins,
-> 1517                                   batch_size=batch_size, verbose=verbose)
   1518 
   1519     def train_on_batch(self, x, y,

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/engine/training.py in _predict_loop(self, f, ins, batch_size, verbose)
   1139                 ins_batch = _slice_arrays(ins, batch_ids)
   1140 
-> 1141             batch_outs = f(ins_batch)
   1142             if not isinstance(batch_outs, list):
   1143                 batch_outs = [batch_outs]

~/.virtualenvs/implicit/lib/python3.5/site-packages/keras/backend/tensorflow_backend.py in __call__(self, inputs)
   2266         updated = session.run(self.outputs + [self.updates_op],
   2267                               feed_dict=feed_dict,
-> 2268                               **self.session_kwargs)
   2269         return updated[:len(self.outputs)]
   2270 

~/.virtualenvs/implicit/lib/python3.5/site-packages/tensorflow/python/client/session.py in run(self, fetches, feed_dict, options, run_metadata)
    787     try:
    788       result = self._run(None, fetches, feed_dict, options_ptr,
--> 789                          run_metadata_ptr)
    790       if run_metadata:
    791         proto_data = tf_session.TF_GetBuffer(run_metadata_ptr)

~/.virtualenvs/implicit/lib/python3.5/site-packages/tensorflow/python/client/session.py in _run(self, handle, fetches, feed_dict, options, run_metadata)
    995     if final_fetches or final_targets:
    996       results = self._do_run(handle, final_targets, final_fetches,
--> 997                              feed_dict_string, options, run_metadata)
    998     else:
    999       results = []

~/.virtualenvs/implicit/lib/python3.5/site-packages/tensorflow/python/client/session.py in _do_run(self, handle, target_list, fetch_list, feed_dict, options, run_metadata)
   1130     if handle is None:
   1131       return self._do_call(_run_fn, self._session, feed_dict, fetch_list,
-> 1132                            target_list, options, run_metadata)
   1133     else:
   1134       return self._do_call(_prun_fn, self._session, handle, feed_dict,

~/.virtualenvs/implicit/lib/python3.5/site-packages/tensorflow/python/client/session.py in _do_call(self, fn, *args)
   1137   def _do_call(self, fn, *args):
   1138     try:
-> 1139       return fn(*args)
   1140     except errors.OpError as e:
   1141       message = compat.as_text(e.message)

~/.virtualenvs/implicit/lib/python3.5/site-packages/tensorflow/python/client/session.py in _run_fn(session, feed_dict, fetch_list, target_list, options, run_metadata)
   1119         return tf_session.TF_Run(session, options,
   1120                                  feed_dict, fetch_list, target_list,
-> 1121                                  status, run_metadata)
   1122 
   1123     def _prun_fn(session, handle, feed_dict, fetch_list):

KeyboardInterrupt: 


















In [ ]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)























Evaluating the model













In [ ]:



    


w_sample_prior = prior.rvs(size=128)
eps = np.random.randn(256, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(128), np.ones(256)))

















In [ ]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [ ]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax1.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax1.set_xlabel('$w_1$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

ax2.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap=plt.cm.magma)
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()

















In [ ]:



    


eps = np.random.randn(5000, NOISE_DIM)
w_sample_posterior = inference.predict(eps)

















In [ ]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax1.scatter(*inference.predict(eps[::10]).T, 
            s=4.**2, alpha=.6, cmap='coolwarm_r')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

sns.kdeplot(*inference.predict(eps).T,
            cmap='magma', ax=ax2)

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()

















In [107]:



    


output = expit(np.random.randn(256))
target = np.hstack((np.zeros(128), np.ones(128)))

















In [108]:



    


2*K.mean(K.binary_crossentropy(output=K.constant(output), 
                      target=K.constant(target))).eval(session=sess)




















Out[108]:








1.7183432579040527



















In [109]:



    


np.mean(-np.log(output[128:])-np.log(1-output[:128]))




















Out[109]:








1.7183431791525026



















In [94]:



    


(-np.log(output[:128])-np.log(1-output[128:])).shape




















Out[94]:








(128,)



















In [74]:



    


p1[:128][0]




















Out[74]:








0.343090641899925



















In [73]:



    


p1[128:][0]




















Out[73]:








0.50225667608674573



















In [113]:



    


ratio_estimator.get_weights()[0]




















Out[113]:








array([[ 0.34,  0.75, -0.56, -0.46,  0.04,  0.25, -0.64, -0.32,  0.05,  0.67],
       [-0.38, -0.27,  0.19,  0.55, -0.63, -0.96, -0.27, -0.75,  0.82, -0.13]], dtype=float32)



















In [ ]:



    


 












    

  


    

    
Variational Inference with Implicit Approximate Inference Models (WIP Pt. 8)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.optimizers import Adam
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import HTML, SVG, display_html
from tqdm import tnrange, tqdm_notebook


























Using TensorFlow backend.



















In [3]:



    


# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


K.tf.__version__




















Out[5]:








'1.2.1'



















In [6]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3
PRETRAIN_EPOCHS = 60























Bayesian Logistic Regression (Synthetic Data)













In [7]:



    


w_min, w_max = -5, 5

















In [8]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [9]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[9]:








(300, 300, 2)



















In [10]:



    


prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)

















In [11]:



    


log_prior = prior.logpdf(w_grid)
log_prior.shape




















Out[11]:








(300, 300)



















In [12]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [13]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([  .5, -1.])

















In [14]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[14]:








(3, 2)



















In [15]:



    


y1 = 1
y2 = 1
y3 = 0

















In [16]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[16]:








(3,)



















In [17]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))

















In [18]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[18]:








(300, 300, 3)



















In [19]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [20]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [21]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Model Definitions



















Density Ratio Estimator (Discriminator) Model



















$T_{\psi}(x, z)$


Here we consider


$T_{\psi}(w)$


$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$













In [22]:



    


discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer=Adam(lr=LEARNING_RATE),
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])

















In [23]:



    


ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)

















In [24]:



    


SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[24]:






G
139996050319736
dense_1_input: InputLayerinput:output:(None, 2)(None, 2)139996049881464
dense_1: Denseinput:output:(None, 2)(None, 10)139996050319736->139996049881464
139996049882416
dense_2: Denseinput:output:(None, 10)(None, 20)139996049881464->139996049882416
139996050321304
logit: Denseinput:output:(None, 20)(None, 1)139996049882416->139996050321304
139996050741624
activation_1: Activationinput:output:(None, 1)(None, 1)139996050321304->139996050741624



















In [25]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)























Initial density ratio, prior to any training













In [26]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [27]:



    


discriminator.evaluate(prior.rvs(size=5), np.zeros(5))


























5/5 [==============================] - 0s











Out[27]:








[0.62235820293426514, 0.60000002384185791]

























Approximate Inference Model



















$z_{\phi}(x, \epsilon)$


Here we only consider


$z_{\phi}(\epsilon)$


$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$













In [28]:



    


inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()


























_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

























The variational parameters $\phi$ are the trainable weights of the approximate inference model













In [29]:



    


phi = inference.trainable_weights
phi




















Out[29]:








[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]



















In [30]:



    


SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[30]:






G
139996049667352
dense_3_input: InputLayerinput:output:(None, 3)(None, 3)139996049443528
dense_3: Denseinput:output:(None, 3)(None, 10)139996049667352->139996049443528
139996049443416
dense_4: Denseinput:output:(None, 10)(None, 20)139996049443528->139996049443416
139996049667520
dense_5: Denseinput:output:(None, 20)(None, 2)139996049443416->139996049667520



















In [31]:



    


w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape




















Out[31]:








(200, 2)



















In [32]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape




















Out[32]:








(200, 2)



















In [33]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [34]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [35]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [36]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [37]:



    


metrics




















Out[37]:








[0.69308857917785649, 0.47749999999999998]



















In [38]:



    


metrics_dict = dict(zip(discriminator.metrics_names, metrics))

















In [39]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

metrics_plots = {k:ax1.plot([], label=k)[0] 
                 for k in ['loss']} # discriminator.metrics_names}

ax1.set_xlabel('epoch')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()



















































Discriminator pre-training













In [40]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, steps_per_epoch=15):

    # Single training epoch
    
    for step in tnrange(steps_per_epoch, unit='step', leave=False):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    # Plot Metrics
        
    metrics_dict = dict(zip(discriminator.metrics_names, metrics))

    for metric in metrics_plots:
        metrics_plots[metric].set_xdata(np.append(metrics_plots[metric].get_xdata(), 
                                                  epoch_num))    
        metrics_plots[metric].set_ydata(np.append(metrics_plots[metric].get_ydata(), 
                                                  metrics_dict[metric]))
        metrics_plots[metric].set_label('{} ({:.2f})' \
                                        .format(metric, 
                                                metrics_dict[metric]))
    
    ax1.set_xlabel('epoch {:2d}'.format(epoch_num))
    ax1.legend(loc='upper left')

    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(**metrics_dict)

    return list(metrics_plots.values())

















In [41]:



    


# main training loop is managed by higher-order
# FuncAnimation which makes calls to an `animate` 
# function that encapsulates the logic of single
# training epoch. Has benefit of producing 
# animation but can incur significant overhead
with tqdm_notebook(total=PRETRAIN_EPOCHS, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=PRETRAIN_EPOCHS,
                         interval=200, # 5 fps
                         blit=True)

    anim_html5_video = anim.to_html5_video()


























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In [42]:



    


HTML(anim_html5_video)




















Out[42]:

























In [43]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [44]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [45]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [46]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

metrics_dict = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**metrics_dict), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Evidence lower bound













In [47]:



    


def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)

















In [48]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[48]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [49]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[49]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [50]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [51]:



    


sess = K.get_session()

















In [52]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[52]:








True



















In [53]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [54]:



    


def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(log_likelihood-kl_estimate, axis=-1)

    return elbo

















In [55]:



    


elbo = make_elbo(ratio_estimator)

















In [56]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [57]:



    


inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)

















In [58]:



    


inference.compile(loss=inference_loss, 
                  optimizer=Adam(lr=LEARNING_RATE))

















In [59]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [60]:



    


y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[60]:








<tf.Tensor 'concat:0' shape=(200, 3) dtype=float32>



















In [61]:



    


sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))




















Out[61]:








-2.5127466



















In [62]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/200 [===>..........................] - ETA: 0s










Out[62]:








2.5127464294433595

























Adversarial Training













In [63]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

global_epoch = 0

loss_plot_inference, = ax1.plot([], label='inference')
loss_plot_discrim, = ax1.plot([], label='discriminator')

ax1.set_xlabel('epoch')
ax1.set_ylabel('loss')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [64]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, 
                  steps_per_epoch=15):

    global global_epoch, loss_plot_inference, loss_plot_discrim
    
    # Single training epoch

    ## Ratio estimator training
        
    set_trainable(discriminator, True)

    for _ in tnrange(3*50, unit='step', desc='discriminator', 
                     leave=False):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)

    metrics_dict_discrim = dict(zip(discriminator.metrics_names, 
                                    np.atleast_1d(metrics_discrim)))
    
    ## Inference model training
    
    set_trainable(ratio_estimator, False)

    y_tiled = np.tile(y, reps=(BATCH_SIZE, 1))

    for _ in tnrange(1, unit='step', desc='inference', leave=False):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, y_tiled)
        
    metrics_dict_inference = dict(zip(inference.metrics_names, 
                                      np.atleast_1d(metrics_inference)))

    global_epoch += 1
    
    # Plot Loss
 
    loss_plot_inference.set_xdata(np.append(loss_plot_inference.get_xdata(),
                                            global_epoch))
    loss_plot_inference.set_ydata(np.append(loss_plot_inference.get_ydata(), 
                                            metrics_dict_inference['loss']))

    loss_plot_inference.set_label('inference ({:.2f})' \
                                  .format(metrics_dict_inference['loss']))

    loss_plot_discrim.set_xdata(np.append(loss_plot_discrim.get_xdata(),
                                          global_epoch))
    loss_plot_discrim.set_ydata(np.append(loss_plot_discrim.get_ydata(),
                                          metrics_dict_discrim['loss']))

    loss_plot_discrim.set_label('discriminator ({:.2f})' \
                                  .format(metrics_dict_discrim['loss']))
    
    ax1.set_xlabel('epoch {:2d}'.format(global_epoch))
    ax1.legend(loc='upper left')
    
    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss_inference=metrics_dict_inference['loss'],
                         loss_discriminator=metrics_dict_discrim['loss'])

    return loss_plot_inference, loss_plot_discrim

















In [65]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Out[65]:

























In [66]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Out[66]:

























In [67]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[67]:

























In [68]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Out[68]:































Evaluating the model













In [81]:



    


w_sample_prior = prior.rvs(size=128)
eps = np.random.randn(256, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(128), np.ones(256)))

















In [82]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [85]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax1.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax1.set_xlabel('$w_1$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

ax2.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap=plt.cm.magma)
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [101]:



    


eps = np.random.randn(5000, NOISE_DIM)
w_sample_posterior = inference.predict(eps)

















In [105]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax1.scatter(*inference.predict(eps[::10]).T, 
            s=4.**2, alpha=.6, cmap='coolwarm_r')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

sns.kdeplot(*inference.predict(eps).T,
            cmap='magma', ax=ax2)

plt.show()








































    

  


    

    
Variational Inference with Implicit Models (forked from @fhuszar)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import theano

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.special import expit
from scipy.stats import logistic

from theano import tensor as T
from theano.tensor.shared_randomstreams import RandomStreams
from theano.printing import debugprint

from lasagne.updates import adam
from lasagne.utils import floatX
from lasagne.nonlinearities import sigmoid
from lasagne.layers import get_output, get_all_params
from lasagne.layers import (InputLayer,
                            DenseLayer,
                            NonlinearityLayer)


from matplotlib.animation import FuncAnimation
from IPython.display import HTML, SVG, display_html
from tqdm import tnrange, tqdm_notebook


























/home/tiao/.virtualenvs/implicit/lib/python3.5/site-packages/theano/tensor/signal/downsample.py:6: UserWarning: downsample module has been moved to the theano.tensor.signal.pool module.
  "downsample module has been moved to the theano.tensor.signal.pool module.")



















In [3]:



    


# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3
PRETRAIN_EPOCHS = 60

















In [6]:



    


PRETRAIN_EPOCHS*15




















Out[6]:








900



















In [7]:



    


w_min, w_max = -5, 5

















In [8]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [9]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[9]:








(300, 300, 2)



















In [10]:



    


log_prior = -.5*np.sum(w_grid**2, axis=2)/PRIOR_VARIANCE
log_prior.shape




















Out[10]:








(300, 300)



















In [11]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [12]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([  .5, -1.])

















In [13]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[13]:








(3, 2)



















In [14]:



    


y1 = 1
y2 = 1
y3 = -1

















In [15]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[15]:








(3,)



















In [16]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return logistic.logcdf(y*(np.dot(w.T,x)))

















In [17]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[17]:








(300, 300, 3)



















In [18]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [19]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [20]:



    


# unnormalised log posterior
# only for illustration purposes
log_post = log_prior + np.sum(llhs, axis=2)

















In [21]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_post), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Fitting an approximate posterior



This part is for the actual GAN stuff. Here we define the generator and the discriminator networks in Lasagne, and code up the two loss functions in theano.













In [22]:



    


#defines a 'generator' network
def build_G(input_var=None, num_z = 3):
    
    network = InputLayer(input_var=input_var, shape=(None, num_z))
    
    network = DenseLayer(incoming = network, num_units=10)
    
    network = DenseLayer(incoming = network, num_units=20)
    
    network = DenseLayer(incoming = network, num_units=2, nonlinearity=None)
    
    return network

















In [23]:



    


#defines the 'discriminator network'
def build_D(input_var=None):

    network = InputLayer(input_var=input_var, shape = (None, 2))
    
    network = DenseLayer(incoming = network, num_units=10)
    
    network = DenseLayer(incoming = network, num_units=20)
    
    network = DenseLayer(incoming = network, num_units=1, nonlinearity=None)
    
    normalised = NonlinearityLayer(incoming = network, nonlinearity = sigmoid)
    
    return { 'unnorm':network, 'norm':normalised }

















In [71]:



    


#variables for input (design matrix), output labels, GAN noise variable, weights
x_var = T.matrix('design matrix')
y_var = T.vector('labels')
z_var = T.matrix('GAN noise')
w_var = T.matrix('weights')

#theano variables for things like batchsize, learning rate, etc.
batchsize_var = T.scalar('batchsize', dtype='int32')
prior_variance_var = T.scalar('prior variance')
learningrate_var = T.scalar('learning rate')

#random numbers for sampling from the prior or from the GAN
srng = RandomStreams(seed=13574437)
z_rnd = srng.normal((batchsize_var,3))
prior_rnd = srng.normal((batchsize_var,2))

#instantiating the G and D networks
generator = build_G(z_var)
discriminator = build_D()

#these expressions are random samples from the generator and the prior, respectively
samples_from_grenerator = get_output(generator, z_rnd)
samples_from_prior = prior_rnd*T.sqrt(prior_variance_var)

#discriminator output for synthetic samples, both normalised and unnormalised (after/before sigmoid)
D_of_G = get_output(discriminator['norm'], inputs=samples_from_grenerator)
s_of_G = get_output(discriminator['unnorm'], inputs=samples_from_grenerator)

#discriminator output for real samples from the prior
D_of_prior = get_output(discriminator['norm'], inputs=samples_from_prior)

#loss of discriminator - simple binary cross-entropy loss
loss_D = -T.log(D_of_G).mean() - T.log(1-D_of_prior).mean()

#log likelihood for each synthetic w sampled from the generator
log_likelihood = T.log(
    T.nnet.sigmoid(
        (y_var.dimshuffle(0,'x','x')*(x_var.dimshuffle(0,1,'x') * samples_from_grenerator.dimshuffle('x', 1, 0))).sum(1)
    )
).sum(0).mean()

#loss for G is the sum of unnormalised discriminator output and the negative log likelihood
loss_G = s_of_G.mean() - log_likelihood

#compiling theano functions:
evaluate_generator = theano.function(
    [z_var],
    get_output(generator),
    allow_input_downcast=True
)

sample_generator = theano.function(
    [batchsize_var],
    samples_from_grenerator,
    allow_input_downcast=True,
)

sample_prior = theano.function(
    [prior_variance_var, batchsize_var],
    samples_from_prior,
    allow_input_downcast=True
)

params_D = get_all_params(discriminator['norm'], trainable=True)

updates_D = adam(
    loss_D,
    params_D,
    learning_rate = learningrate_var
)

train_D = theano.function(
    [learningrate_var, batchsize_var, prior_variance_var],
    loss_D,
    updates = updates_D,
    allow_input_downcast = True
)

params_G = get_all_params(generator, trainable=True)

updates_G = adam(
    loss_G,
    params_G,
    learning_rate = learningrate_var
)

train_G = theano.function(
    [x_var, y_var, learningrate_var, batchsize_var],
    loss_G,
    updates = updates_G,
    allow_input_downcast = True
)

evaluate_discriminator = theano.function(
    [w_var],
    get_output([discriminator['unnorm'],discriminator['norm']],w_var),
    allow_input_downcast = True
)

#this is to evaluate the log-likelihood of an arbitrary set of w
llh_for_w = T.nnet.sigmoid((y_var.dimshuffle(0,'x','x')*(x_var.dimshuffle(0,1,'x') * w_var.dimshuffle('x', 1, 0))).sum(1))

evaluate_loglikelihood = theano.function(
        [x_var, y_var, w_var],
        llh_for_w,
        allow_input_downcast = True
    )

















In [72]:



    


w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300,300)

















In [73]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [74]:



    


w_sample_prior = sample_prior(PRIOR_VARIANCE, BATCH_SIZE)
w_sample_posterior = sample_generator(BATCH_SIZE)

















In [75]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [76]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.exp(log_post), cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [77]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

loss_plot, = ax1.plot([], label='loss')

ax1.set_xlabel('epoch')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [78]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, steps_per_epoch=15):

    # Single training epoch
    
    for step in tnrange(steps_per_epoch, unit='step', leave=False):
        
        loss = np.asscalar(train_D(LEARNING_RATE, 
                                   batch_size, 
                                   PRIOR_VARIANCE))

    # Plot Loss

    loss_plot.set_xdata(np.append(loss_plot.get_xdata(), epoch_num))    
    loss_plot.set_ydata(np.append(loss_plot.get_ydata(), loss))
    loss_plot.set_label('loss ({:.2f})'.format(loss))
    
    ax1.set_xlabel('epoch {:2d}'.format(epoch_num))
    ax1.legend(loc='upper left')

    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()
        
    w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300,300)
    
    w_sample_prior = sample_prior(PRIOR_VARIANCE, batch_size)
    w_sample_posterior = sample_generator(batch_size)

    inputs = np.vstack((w_sample_prior, w_sample_posterior))
    targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))
    
    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss=loss)

    return loss_plot,

















In [79]:



    


# main training loop is managed by higher-order
# FuncAnimation which makes calls to an `animate` 
# function that encapsulates the logic of single
# training epoch. Has benefit of producing 
# animation but can incur significant overhead
with tqdm_notebook(total=PRETRAIN_EPOCHS, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=PRETRAIN_EPOCHS,
                         interval=200, # 5 fps
                         blit=True)

    anim_html5_video = anim.to_html5_video()


























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In [80]:



    


HTML(anim_html5_video)




















Out[80]:

























In [81]:



    


fig, ax = plt.subplots(figsize=(5, 5))

w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300,300)

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Adversarial Training













In [82]:



    


llh_theano = evaluate_loglikelihood(X, y, w_grid.reshape(300*300, 2))
llh_theano.shape




















Out[82]:








(3, 90000)



















In [83]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap='magma')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)
ax1.set_title('numpy loglikelihood')

ax2.contourf(w1, w2, np.sum(np.log(llh_theano), 0).reshape(300,300), 
             cmap='magma')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)
ax2.set_title('theano loglikelihood')

plt.show()













































In [84]:



    


np.allclose(np.sum(llhs, axis=2),
            np.sum(np.log(llh_theano), 0).reshape(300,300))




















Out[84]:








True



















In [85]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

global_epoch = 0

loss_plot_inference, = ax1.plot([], label='inference')
loss_plot_discrim, = ax1.plot([], label='discriminator')

ax1.set_xlabel('epoch')
ax1.set_ylabel('loss')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [86]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, 
                  steps_per_epoch=15):

    global global_epoch, loss_plot_inference, loss_plot_discrim
    
    # Single training epoch

    ## Ratio estimator training

    for _ in tnrange(150, unit='step', desc='discriminator', 
                     leave=False):

        loss_d = np.asscalar(train_D(LEARNING_RATE, 
                                     batch_size, 
                                     PRIOR_VARIANCE))
    
    ## Inference model training

    for _ in tnrange(1, unit='step', desc='inference', leave=False):

        loss_g = np.asscalar(train_G(X, y, LEARNING_RATE, batch_size))

    global_epoch += 1

    # Plot Loss

    loss_plot_discrim.set_xdata(np.append(loss_plot_discrim.get_xdata(), global_epoch))
    loss_plot_discrim.set_ydata(np.append(loss_plot_discrim.get_ydata(), loss_d))
    loss_plot_discrim.set_label('discriminator ({:.2f})'.format(loss_d))
    
    loss_plot_inference.set_xdata(np.append(loss_plot_inference.get_xdata(), global_epoch))    
    loss_plot_inference.set_ydata(np.append(loss_plot_inference.get_ydata(), loss_g))
    loss_plot_inference.set_label('inference ({:.2f})'.format(loss_g))

    ax1.set_xlabel('epoch {:2d}'.format(global_epoch))
    ax1.legend(loc='upper left')
    
    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()
        
    w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300,300)
    
    w_sample_prior = sample_prior(PRIOR_VARIANCE, batch_size)
    w_sample_posterior = sample_generator(batch_size)

    inputs = np.vstack((w_sample_prior, w_sample_posterior))
    targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))
    
    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)

    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss_g=loss_g, loss_d=loss_d)

    return loss_plot_inference, loss_plot_discrim

















In [87]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[87]:

























In [88]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[88]:

























In [89]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[89]:

























In [90]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Out[90]:

























In [ ]:



    


 

















In [45]:



    


plt.figure(figsize=(16,8))


plt.subplot(1,2,1)
plt.contourf(wrange, wrange, evaluate_discriminator(w.T)[0].reshape(300,300).T)

W = sample_generator(100)
plt.plot(W[:,0],W[:,1],'g.')

W = sample_prior(prior_variance, 100)
plt.plot(W[:,0],W[:,1],'r.')
plt.axis('square')
plt.xlim([wmin,wmax])
plt.ylim([wmin,wmax])
plt.title('estimated log density ratio $\Phi^{-1}(D)$')

plt.subplot(1,2,2)
plt.contourf(wrange, wrange, (llh1+llh2+llh3).reshape(300,300).T)
plt.axis('square')
plt.xlim([wmin,wmax])
plt.ylim([wmin,wmax]);

plt.title('log likelihood');


























---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-45-00c7d0990f48> in <module>()
      3 
      4 plt.subplot(1,2,1)
----> 5 plt.contourf(wrange, wrange, evaluate_discriminator(w.T)[0].reshape(300,300).T)
      6 
      7 W = sample_generator(100)

NameError: name 'wrange' is not defined



































In [ ]:



    


plt.figure(figsize=(16,8))
plt.subplot(1,2,1)
plt.axis('square');
plt.xlim([w_min,w_max])
plt.ylim([w_min,w_max])
plt.title('theano loglikelihood')

plt.subplot(1,2,2)
plt.contourf(w1, w2, (llh1+llh2+llh3).reshape(300,300).T,cmap='gray');
plt.axis('square');
plt.xlim([w_min,w_max])
plt.ylim([w_min,w_max])
plt.title('numpy loglikelihood')

assert np.allclose(llh1+llh2+llh3,np.log(llh_theano).sum(0))

















In [ ]:



    


plt.figure(figsize=(16,8))


plt.subplot(1,2,1)
plt.contourf(wrange, wrange, evaluate_discriminator(w.T)[0].reshape(300,300).T)

W = sample_generator(100)
plt.plot(W[:,0],W[:,1],'g.')

W = sample_prior(prior_variance, 100)
plt.plot(W[:,0],W[:,1],'r.')
plt.axis('square')
plt.xlim([wmin,wmax])
plt.ylim([wmin,wmax])
plt.title('estimated log density ratio $\Phi^{-1}(D)$')

plt.subplot(1,2,2)
plt.contourf(wrange, wrange, (llh1+llh2+llh3).reshape(300,300).T)
plt.axis('square')
plt.xlim([wmin,wmax])
plt.ylim([wmin,wmax]);

plt.title('log likelihood');

















In [ ]:



    


X_train = np.concatenate([x1,x2,x3],axis=1).T
y_train = np.array([y1,y2,y3])
llh_theano = evaluate_loglikelihood(X_train, y_train, w.T)

plt.figure(figsize=(16,8))
plt.subplot(1,2,1)
plt.contourf(wrange, wrange ,np.log(llh_theano).sum(0).reshape(300,300).T,cmap='gray');
plt.axis('square');
plt.xlim([wmin,wmax])
plt.ylim([wmin,wmax])
plt.title('theano loglikelihood')

plt.subplot(1,2,2)
plt.contourf(wrange, wrange, (llh1+llh2+llh3).reshape(300,300).T,cmap='gray');
plt.axis('square');
plt.xlim([wmin,wmax])
plt.ylim([wmin,wmax])
plt.title('numpy loglikelihood')

assert np.allclose(llh1+llh2+llh3,np.log(llh_theano).sum(0))

















In [ ]:



    


plt.contourf(wrange, wrange, np.exp(logpost.reshape(300,300).T),cmap='gray');
plt.axis('square');
W = sample_generator(1000)
plt.plot(W[:,0],W[:,1],'.g')
plt.xlim([wmin,wmax])
plt.ylim([wmin,wmax]);
plt.title('true log posterior');

















In [ ]:



    


sns.set_style('whitegrid')
plt.subplot(1,2,2)

W = sample_generator(5000)
plot = sns.kdeplot(W[:,0],W[:,1])
plt.axis('square')
plot.set(xlim=(wmin,wmax))
plot.set(ylim=(wmin,wmax))
plt.title('kde of approximate posterior')

plt.subplot(1,2,1)
plt.contourf(wrange, wrange, np.exp(logpost.reshape(300,300).T),cmap='gray');
plt.axis('square');
W = sample_generator(100)
plt.plot(W[:,0],W[:,1],'.g')
plt.xlim([wmin,wmax])
plt.ylim([wmin,wmax]);
plt.title('true posterior');

















In [ ]:



    


 












    

  


    

    
Variational Inference with Implicit Approximate Inference Models (WIP Pt. 7)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.optimizers import Adam
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import SVG
from tqdm import tnrange


























Using TensorFlow backend.



















In [3]:



    


# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


K.tf.__version__




















Out[5]:








'1.2.1'



















In [6]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3























Bayesian Logistic Regression (Synthetic Data)













In [7]:



    


w_min, w_max = -5, 5

















In [8]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [9]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[9]:








(300, 300, 2)



















In [10]:



    


prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)

















In [11]:



    


log_prior = prior.logpdf(w_grid)
log_prior.shape




















Out[11]:








(300, 300)



















In [12]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [13]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([  .5, -1.])

















In [14]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[14]:








(3, 2)



















In [15]:



    


y1 = 1
y2 = 1
y3 = 0

















In [16]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[16]:








(3,)



















In [17]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))

















In [18]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[18]:








(300, 300, 3)



















In [19]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [20]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [21]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Model Definitions



















Density Ratio Estimator (Discriminator) Model



















$T_{\psi}(x, z)$


Here we consider


$T_{\psi}(w)$


$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$













In [22]:



    


discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer=Adam(lr=LEARNING_RATE),
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])

















In [23]:



    


ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)

















In [24]:



    


SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[24]:






G
4729044328
dense_1_input: InputLayerinput:output:(None, 2)(None, 2)4727278616
dense_1: Denseinput:output:(None, 2)(None, 10)4729044328->4727278616
4729043432
dense_2: Denseinput:output:(None, 10)(None, 20)4727278616->4729043432
4729057176
logit: Denseinput:output:(None, 20)(None, 1)4729043432->4729057176
4721891144
activation_1: Activationinput:output:(None, 1)(None, 1)4729057176->4721891144



















In [25]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)























Initial density ratio, prior to any training













In [26]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [27]:



    


discriminator.evaluate(prior.rvs(size=5), np.zeros(5))


























5/5 [==============================] - 0s











Out[27]:








[0.53143018484115601, 1.0]

























Approximate Inference Model



















$z_{\phi}(x, \epsilon)$


Here we only consider


$z_{\phi}(\epsilon)$


$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$













In [28]:



    


inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()


























_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

























The variational parameters $\phi$ are the trainable weights of the approximate inference model













In [29]:



    


phi = inference.trainable_weights
phi




















Out[29]:








[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]



















In [30]:



    


SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[30]:






G
4732353784
dense_3_input: InputLayerinput:output:(None, 3)(None, 3)4732435816
dense_3: Denseinput:output:(None, 3)(None, 10)4732353784->4732435816
4732434640
dense_4: Denseinput:output:(None, 10)(None, 20)4732435816->4732434640
4716115280
dense_5: Denseinput:output:(None, 20)(None, 2)4732434640->4716115280



















In [31]:



    


w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape




















Out[31]:








(200, 2)



















In [32]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape




















Out[32]:








(200, 2)



















In [33]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [34]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [35]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [36]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [37]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)




















Out[37]:








(-5, 5)










































Discriminator pre-training













In [38]:



    


def train_animate(epoch_num, batch_size=200, steps_per_epoch=15):

    for step in range(steps_per_epoch):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    ax.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

    ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    train_info = dict(zip(discriminator.metrics_names, metrics))
    train_info['epoch'] = epoch_num
    
    props = dict(boxstyle='round', facecolor='w', alpha=0.5)

    ax.text(0.05, 0.05, 
            ('epoch: {epoch:2d}\n'
             'accuracy: {binary_accuracy:.2f}\n'        
             'loss: {loss:.2f}').format(**train_info), 
            transform=ax.transAxes, bbox=props)

    ax.set_xlabel('$w_1$')
    ax.set_ylabel('$w_2$')

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    return ax

















In [39]:



    


FuncAnimation(fig, train_animate, frames=60, 
              interval=200, # 5 fps
              blit=False)




















Out[39]:

























In [40]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [41]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [42]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [43]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Evidence lower bound













In [44]:



    


def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)

















In [45]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[45]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [46]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[46]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [47]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [48]:



    


sess = K.get_session()

















In [49]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[49]:








True



















In [50]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [51]:



    


def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(log_likelihood-kl_estimate, axis=-1)

    return elbo

















In [52]:



    


elbo = make_elbo(ratio_estimator)

















In [53]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [54]:



    


inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)

















In [55]:



    


inference.compile(loss=inference_loss, 
                  optimizer=Adam(lr=LEARNING_RATE))

















In [56]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [57]:



    


y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[57]:








<tf.Tensor 'concat:0' shape=(200, 3) dtype=float32>



















In [58]:



    


sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))




















Out[58]:








-3.8279114



















In [59]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/200 [===>..........................] - ETA: 0s










Out[59]:








3.8279113578796387

























Training













In [60]:



    


for epoch in tnrange(200, desc='epoch'):

    set_trainable(ratio_estimator, False)

    for _ in tnrange(1, desc='generator'):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, np.tile(y, reps=(BATCH_SIZE, 1)))

    set_trainable(discriminator, True)

    for _ in tnrange(3*50, desc='discriminator'):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)


























 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 







































In [61]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [62]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [63]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [64]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.gray)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()








































    

  


    

    
My PhD in Weeks

        

            

            

                
            Comments


        



    

    



This is your PhD, and it's ending one week at a time.













 
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Variational Inference with Implicit Approximate Inference Models (WIP Pt. 6)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import SVG


























Using TensorFlow backend.



















In [3]:



    


plt.style.use('seaborn-notebook')
# display animation inline
plt.rc('animation', html='html5')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


K.tf.__version__




















Out[5]:








'1.2.1'



















In [6]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 128
PRIOR_VARIANCE = 2.























Bayesian Logistic Regression (Synthetic Data)













In [7]:



    


w_min, w_max = -5, 5

















In [8]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [9]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[9]:








(300, 300, 2)



















In [10]:



    


prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)

















In [11]:



    


log_prior = prior.logpdf(w_grid)
log_prior.shape




















Out[11]:








(300, 300)



















In [12]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [13]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([- .5, -1.])

















In [14]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[14]:








(3, 2)



















In [15]:



    


y1 = 1
y2 = 1
y3 = 0

















In [16]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[16]:








(3,)



















In [17]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))

















In [18]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[18]:








(300, 300, 3)



















In [19]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [20]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [21]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Model Definitions



















Density Ratio Estimator (Discriminator) Model



















$T_{\psi}(x, z)$


Here we consider


$T_{\psi}(w)$


$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$













In [22]:



    


discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer='adam',
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])

















In [23]:



    


ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)

















In [24]:



    


SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[24]:






G
4766144608
dense_1_input: InputLayerinput:output:(None, 2)(None, 2)4766145224
dense_1: Denseinput:output:(None, 2)(None, 10)4766144608->4766145224
4767336208
dense_2: Denseinput:output:(None, 10)(None, 20)4766145224->4767336208
4766143992
logit: Denseinput:output:(None, 20)(None, 1)4767336208->4766143992
4766535464
activation_1: Activationinput:output:(None, 1)(None, 1)4766143992->4766535464



















In [25]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)























Initial density ratio, prior to any training













In [26]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [27]:



    


discriminator.evaluate(prior.rvs(size=5), np.zeros(5))


























5/5 [==============================] - 0s











Out[27]:








[0.72363483905792236, 0.40000000596046448]

























Approximate Inference Model



















$z_{\phi}(x, \epsilon)$


Here we only consider


$z_{\phi}(\epsilon)$


$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$













In [28]:



    


inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()


























_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

























The variational parameters $\phi$ are the trainable weights of the approximate inference model













In [29]:



    


phi = inference.trainable_weights
phi




















Out[29]:








[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]



















In [30]:



    


SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[30]:






G
4769765752
dense_3_input: InputLayerinput:output:(None, 3)(None, 3)4769787520
dense_3: Denseinput:output:(None, 3)(None, 10)4769765752->4769787520
4769190184
dense_4: Denseinput:output:(None, 10)(None, 20)4769787520->4769190184
4769949288
dense_5: Denseinput:output:(None, 20)(None, 2)4769190184->4769949288



















In [31]:



    


w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape




















Out[31]:








(128, 2)



















In [32]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape




















Out[32]:








(128, 2)



















In [33]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [34]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [35]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [36]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [37]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Discriminator pre-training













In [38]:



    


def train_animate(epoch_num, batch_size=128, steps_per_epoch=20):

    for step in range(steps_per_epoch):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    ax.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

    ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

    train_info = dict(zip(discriminator.metrics_names, metrics))
    train_info['epoch'] = epoch_num
    
    props = dict(boxstyle='round', facecolor='w', alpha=0.5)

    ax.text(0.05, 0.05, 
            ('epoch: {epoch:2d}\n'
             'accuracy: {binary_accuracy:.2f}\n'        
             'loss: {loss:.2f}').format(**train_info), 
            transform=ax.transAxes, bbox=props)

    ax.set_xlabel('$w_1$')
    ax.set_ylabel('$w_2$')

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    return ax

















In [39]:



    


FuncAnimation(fig, train_animate, frames=50, 
              interval=200, # 5 fps
              blit=False)




















Out[39]:

























In [40]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [41]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [42]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [43]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Evidence lower bound













In [44]:



    


def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)

















In [45]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[45]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [46]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[46]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [47]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [48]:



    


sess = K.get_session()

















In [49]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[49]:








True



















In [50]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [51]:



    


def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(log_likelihood-kl_estimate, axis=-1)

    return elbo

















In [52]:



    


elbo = make_elbo(ratio_estimator)

















In [53]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [59]:



    


inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)

















In [60]:



    


inference.compile(loss=inference_loss, 
                  optimizer='adam')

















In [61]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [62]:



    


y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[62]:








<tf.Tensor 'concat_1:0' shape=(128, 3) dtype=float32>



















In [63]:



    


sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))




















Out[63]:








-3.9920437



















In [64]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/128 [======>.......................] - ETA: 0s










Out[64]:








3.9920437335968018

























Training













In [70]:



    


for epoch in range(3*200):

    set_trainable(ratio_estimator, False)

    for _ in range(1):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, np.tile(y, reps=(BATCH_SIZE, 1)))

    set_trainable(discriminator, True)

    for _ in range(3*50):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)

















In [71]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [72]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [73]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [74]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [ ]:



    


 












    

  


    

    
Variational Inference with Implicit Approximate Inference Models (WIP Pt. 5)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import SVG


























Using TensorFlow backend.



















In [3]:



    


plt.style.use('seaborn-notebook')
# display animation inline
plt.rc('animation', html='html5')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


K.tf.__version__




















Out[5]:








'1.2.1'



















In [6]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 128
D_BATCH_SIZE = 128
G_BATCH_SIZE = 128
PRIOR_VARIANCE = 2.























Bayesian Logistic Regression (Synthetic Data)













In [7]:



    


w_min, w_max = -5, 5

















In [8]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [9]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[9]:








(300, 300, 2)



















In [10]:



    


prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)

















In [11]:



    


log_prior = prior.logpdf(w_grid)
log_prior.shape




















Out[11]:








(300, 300)



















In [12]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [13]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([- .5, -1.])

















In [14]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[14]:








(3, 2)



















In [15]:



    


y1 = 1
y2 = 1
y3 = 0

















In [16]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[16]:








(3,)



















In [17]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))

















In [18]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[18]:








(300, 300, 3)



















In [19]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [20]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [21]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Model Definitions



















Density Ratio Estimator (Discriminator) Model



















$T_{\psi}(x, z)$


Here we consider


$T_{\psi}(w)$


$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$













In [22]:



    


discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer='adam',
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])

















In [23]:



    


ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)

















In [24]:



    


SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[24]:






G
4796441544
dense_1_input: InputLayerinput:output:(None, 2)(None, 2)4797073168
dense_1: Denseinput:output:(None, 2)(None, 10)4796441544->4797073168
4796631920
dense_2: Denseinput:output:(None, 10)(None, 20)4797073168->4796631920
4796443560
logit: Denseinput:output:(None, 20)(None, 1)4796631920->4796443560
4795146192
activation_1: Activationinput:output:(None, 1)(None, 1)4796443560->4795146192



















In [25]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)























Initial density ratio, prior to any training













In [26]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [27]:



    


discriminator.evaluate(prior.rvs(size=5), np.zeros(5))


























5/5 [==============================] - 0s











Out[27]:








[0.63304531574249268, 0.60000002384185791]

























Approximate Inference Model



















$z_{\phi}(x, \epsilon)$


Here we only consider


$z_{\phi}(\epsilon)$


$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$













In [28]:



    


inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()


























_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

























The variational parameters $\phi$ are the trainable weights of the approximate inference model













In [29]:



    


phi = inference.trainable_weights
phi




















Out[29]:








[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]



















In [30]:



    


SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[30]:






G
4783101656
dense_3_input: InputLayerinput:output:(None, 3)(None, 3)4797501680
dense_3: Denseinput:output:(None, 3)(None, 10)4783101656->4797501680
4797502688
dense_4: Denseinput:output:(None, 10)(None, 20)4797501680->4797502688
4799943456
dense_5: Denseinput:output:(None, 20)(None, 2)4797502688->4799943456



















In [31]:



    


w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape




















Out[31]:








(128, 2)



















In [32]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape




















Out[32]:








(128, 2)



















In [33]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [34]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [35]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [36]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [37]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Discriminator pre-training













In [38]:



    


def train_animate(epoch_num, batch_size=128, steps_per_epoch=20):

    for step in range(steps_per_epoch):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    ax.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

    ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

    train_info = dict(zip(discriminator.metrics_names, metrics))
    train_info['epoch'] = epoch_num
    
    props = dict(boxstyle='round', facecolor='w', alpha=0.5)

    ax.text(0.05, 0.05, 
            ('epoch: {epoch:2d}\n'
             'accuracy: {binary_accuracy:.2f}\n'        
             'loss: {loss:.2f}').format(**train_info), 
            transform=ax.transAxes, bbox=props)

    ax.set_xlabel('$w_1$')
    ax.set_ylabel('$w_2$')

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    return ax

















In [39]:



    


FuncAnimation(fig, train_animate, frames=50, 
              interval=200, # 5 fps
              blit=False)




















Out[39]:

























In [40]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [41]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [42]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [43]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Inference Model Training













In [44]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[44]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [45]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[45]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [46]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [47]:



    


sess = K.get_session()

















In [48]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[48]:








True



















In [49]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [50]:



    


def make_elbo(ratio_estimator):

    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(log_likelihood-kl_estimate, axis=-1)

    return elbo

















In [51]:



    


elbo = make_elbo(ratio_estimator)

















In [52]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [94]:



    


inference.compile(loss=make_elbo(ratio_estimator), 
                  optimizer='adam')

















In [95]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [96]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/128 [======>.......................] - ETA: 0s










Out[96]:








-3.2424654364585876



















In [105]:



    


# equiv. to use of tile above
y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[105]:








<tf.Tensor 'concat_10:0' shape=(128, 3) dtype=float32>



















In [107]:



    


sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))




















Out[107]:








-3.2424655














    

  


    

    
Variational Inference with Implicit Approximate Inference Models (WIP Pt. 4)

        

            

            

                
            Comments


        



    

    

    







In [177]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [178]:



    


import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import SVG

















In [179]:



    


plt.style.use('seaborn-notebook')
# display animation inline
plt.rc('animation', html='html5')
sns.set_context('notebook')

















In [180]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [181]:



    


K.tf.__version__




















Out[181]:








'1.2.1'



















In [182]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 128
D_BATCH_SIZE = 128
G_BATCH_SIZE = 128
PRIOR_VARIANCE = 2.























Bayesian Logistic Regression (Synthetic Data)













In [183]:



    


w_min, w_max = -5, 5

















In [184]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [185]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[185]:








(300, 300, 2)



















In [186]:



    


prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)

















In [187]:



    


log_prior = prior.logpdf(w_grid)
log_prior.shape




















Out[187]:








(300, 300)



















In [188]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [189]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([- .5, -1.])

















In [190]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[190]:








(3, 2)



















In [191]:



    


y1 = 1
y2 = 1
y3 = 0

















In [192]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[192]:








(3,)



















In [193]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))

















In [194]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[194]:








(300, 300, 3)



















In [195]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [196]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [197]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Model Definitions



















Density Ratio Estimator (Discriminator) Model



















$T_{\psi}(x, z)$


Here we consider


$T_{\psi}(w)$


$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$













In [22]:



    


discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer='adam',
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])

















In [23]:



    


ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)

















In [24]:



    


SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[24]:






G
140297740092864
dense_1_input: InputLayerinput:output:(None, 2)(None, 2)140297740092640
dense_1: Denseinput:output:(None, 2)(None, 10)140297740092864->140297740092640
140297740091520
dense_2: Denseinput:output:(None, 10)(None, 20)140297740092640->140297740091520
140297740093312
logit: Denseinput:output:(None, 20)(None, 1)140297740091520->140297740093312
140297740622592
activation_1: Activationinput:output:(None, 1)(None, 1)140297740093312->140297740622592



















In [25]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)























Initial density ratio, prior to any training













In [26]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [27]:



    


discriminator.evaluate(prior.rvs(size=5), np.zeros(5))


























5/5 [==============================] - 0s











Out[27]:








[0.63745558261871338, 0.80000001192092896]

























Approximate Inference Model



















$z_{\phi}(x, \epsilon)$


Here we only consider


$z_{\phi}(\epsilon)$


$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$













In [28]:



    


inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()


























_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

























The variational parameters $\phi$ are the trainable weights of the approximate inference model













In [29]:



    


phi = inference.trainable_weights
phi




















Out[29]:








[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]



















In [30]:



    


SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[30]:






G
140297740961440
dense_3_input: InputLayerinput:output:(None, 3)(None, 3)140297740025472
dense_3: Denseinput:output:(None, 3)(None, 10)140297740961440->140297740025472
140297740023568
dense_4: Denseinput:output:(None, 10)(None, 20)140297740025472->140297740023568
140297740591512
dense_5: Denseinput:output:(None, 20)(None, 2)140297740023568->140297740591512



















In [31]:



    


w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape




















Out[31]:








(128, 2)



















In [32]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape




















Out[32]:








(128, 2)



















In [33]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [34]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [35]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [36]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [37]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Discriminator pre-training













In [38]:



    


def train_animate(epoch_num, batch_size=128, steps_per_epoch=20):

    for step in range(steps_per_epoch):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    ax.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

    ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

    train_info = dict(zip(discriminator.metrics_names, metrics))
    train_info['epoch'] = epoch_num
    
    props = dict(boxstyle='round', facecolor='w', alpha=0.5)

    ax.text(0.05, 0.05, 
            ('epoch: {epoch:2d}\n'
             'accuracy: {binary_accuracy:.2f}\n'        
             'loss: {loss:.2f}').format(**train_info), 
            transform=ax.transAxes, bbox=props)

    ax.set_xlabel('$w_1$')
    ax.set_ylabel('$w_2$')

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    return ax

















In [39]:



    


FuncAnimation(fig, train_animate, frames=50, 
              interval=200, # 5 fps
              blit=False)




















Out[39]:

























In [40]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [41]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [42]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [43]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Inference Model Training













In [214]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[214]:








<tf.Tensor 'Sigmoid_13:0' shape=(300, 300, 3) dtype=float32>



















In [215]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[215]:








<tf.Tensor 'mul_50:0' shape=(300, 300, 3) dtype=float32>



















In [207]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [208]:



    


sess = K.get_session()

















In [209]:



    


np.sum(llhs, axis=-1)




















Out[209]:








array([[-20.08, -20.01, -19.94, ...,  -2.72,  -2.69,  -2.66],
       [-20.02, -19.95, -19.88, ...,  -2.68,  -2.64,  -2.61],
       [-19.95, -19.88, -19.81, ...,  -2.63,  -2.6 ,  -2.56],
       ..., 
       [-15.1 , -15.03, -14.96, ...,  -2.55,  -2.52,  -2.49],
       [-15.13, -15.06, -14.99, ...,  -2.59,  -2.56,  -2.53],
       [-15.16, -15.09, -15.02, ...,  -2.64,  -2.61,  -2.58]])



















In [210]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[210]:








True



















In [211]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [216]:



    


def make_elbo(ratio_estimator):

    def elbo(y_true, y_pred):
        log_likelihood = - K.binary_crossentropy(y_pred, y_true)
        kl_estimate = K.mean(ratio_estimator(y_pred), axis=-1)
        return log_likelihood - kl_estimate
    
    return elbo

















In [217]:



    


elbo = make_elbo(ratio_estimator)

















In [ ]: